In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; and e. the missing function values, indicated by question marks, below each graph.

Key Concepts

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In the context of a graph, it is represented by the horizontal extent of the graph. For the given quadratic function, the domain is all real numbers since the graph extends infinitely in both directions along the x-axis.

Range of a Function

The range of a function is the set of all possible output values (y-values) that the function can produce. For a quadratic function that opens upwards, like the one shown, the range starts from the minimum point of the graph and extends to positive infinity. In this case, the range is all real numbers greater than or equal to the y-coordinate of the vertex.

Function Values

Function values are the outputs of a function corresponding to specific inputs. In the context of the graph, missing function values can be determined by identifying the y-coordinates at given x-coordinates. For example, if the graph indicates points where the function's value is unknown, one can find these values by observing the graph's height at those x-values.